The main assumption underlying our proposed model is the existence of a hidden low-dimensional continuous latent space that can explain the observed data. We model the observations as conditionally multinomial distributed given the latent variables, which are assumed to be multivariate Gaussian with low rank covariance structure. Due to the lack of conjugacy between the Gaussian and multinomial distributions, exact Bayes inference is not tractable. We therefore adopt a Bayes variational inference approach [1]}, [2]} to develop an algorithm for estimating the parameters of the proposed model and projecting the data to the latent space.
